If I'm using a VW mod, I'll keep it between six to seven watts. However, I am generally using a provari, so I can only change voltage
When you are using a VV device, such as a Provari, when you change the voltage, you are changing wattage.
Actually, the opposite of what you're saying is true. For a given wattage, there will be less battery draw if you use a higher resistance coil and higher voltage, than you will a low resistance coil and lower volts.
Here's a hypothetical example:
Suppose you have a 3.0 ohm coil, and wish to vape it at 7.0 watts.
In order to do that, you would set your Provari at about 4.6 volts.
At 4.6 volts, 3.0 ohm coil, and 7.0 watts, your amperage draw on your battery is 1.5 amps.
Now, suppose you had a 1.5 ohm coil, and wanted to vape at the same 7.0 watts.
You would now set your Provari at 3.2 volts.
At 3.2 volts, 1.5 ohm coil, and 7.0 watts, your amperage draw on your battery would now be about 2.2 amps.
Obviously, a battery drawing 2.2 amps will discharge faster than one drawing 1.5 amps.